Mariupol was the scene of fierce fighting before a ceasefire took hold last Friday.
It was also the scene of the most serious violation of the ceasefire Saturday night when government forces there came under artillery attack.
Poroshenko vows to defend it from pro-Russian separatists.
“Let everyone know that we will protect our city,” he said. “We will protect our region. We will protect our state and we will not give it away to anyone. We will not give to anybody any bit of Ukrainian land, sovereignty, its territorial integrity, its independence. And now we are fighting for our independence.”
His comments come as the US and Ukraine are conducting joint exercises in the Black Sea.